Foundations of Physics

, Volume 44, Issue 12, pp 1369–1380

Non-reflexive Logical Foundation for Quantum Mechanics

Article

DOI: 10.1007/s10701-014-9848-3

Cite this article as:
da Costa, N.C.A. & de Ronde, C. Found Phys (2014) 44: 1369. doi:10.1007/s10701-014-9848-3

Abstract

On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity.

Keywords

Identity Non-reflexive logic Interpretation of quantum mechanics 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Universidade Federal de Santa CatarinaFlorianopolisBrazil
  2. 2.University of Buenos Aires, CONICETBuenos AiresArgentina
  3. 3.Center Leo Apostel (CLEA) and Foundations of the Exact Sciences (FUND)Brussels Free UniversityBrusselsBelgium

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